All-fiber Faraday Devices Based On Terbium-doped Fiber
All-fiber Faraday Devices Based onTerbium-doped FiberbyLei SunSubmitted in Partial Fulfillmentof theRequirements for the DegreeDoctor of Philosophysupervised byProfessor John R. MarcianteThe Institute of OpticsArts, Sciences and EngineeringEdmund A. Hajim School of Engineering and Applied SciencesUniversity of RochesterRochester, New York2010
iiCurriculum VitaeThe author was born in Tanggu, Tianjin, China, in 1978. He began his undergraduate studies in 1997 at the Physics Department of Nankai University, Tianjin,China, and received his B.S. degree in Applied Optics in 2001. In the same year,he entered the M.S. program at the Institute of Modern Optics, Nankai University,where he studied the fabrication and application of optical fiber gratings under theguidance of Prof. Xiaoyi Dong and received his M.S. degree in Optics in 2004. Hestarted his graduate studies at the Institute of Optics, University of Rochester, in2004. In 2005, the author began his doctoral research at the Laboratory for LaserEnergetics, University of Rochester, where he studied all-fiber Faraday componentsand filamentation in large-mode-area fiber lasers under the guidance of Prof. JohnR. Marciante.
iiiPublicationsJournal Publications L. Sun, S. Jiang, and J. R. Marciante, ”Compact all-fiber optical Faradaycomponents using 65-wt% terbium doped fiber with a record Verdet constantof -32 rad/(Tm),” Opt. Express 18, 12191-12196 (2010) L. Sun, S. Jiang, and J. R. Marciante, ”All-fiber optical Faraday mirrorusing 56-wt% terbium-doped fiber,” IEEE Photon. Technol. Lett. 22, 9991001 (2010) L. Sun, S. Jiang, and J. R. Marciante, ”All-fiber optical magnetic-field sensorbased on Faraday rotation in highly terbium-doped fiber,” Opt. Express 18,5407-5412 (2010), highlighted by Nature Photonics, 4, 425 (2010) L. Sun, S. Jiang, J. D. Zuegel, and J. R. Marciante, ”All-fiber optical isolatorbased on Faraday rotation in highly terbium-doped fiber,” Opt. Lett. 35,706-708 (2010) L. Sun, S. Jiang, J. D. Zuegel, and J. R. Marciante, ”Effective Verdet constant in a terbium-doped-core phosphate fiber,” Opt. Lett. 34, 1699-1701(2009) L. Sun and J. R. Marciante, ”Filamentation analysis in large-mode-areafiber lasers,” J. Opt. Soc. Am. B 24, 2321-2326 (2007) L. Sun, X. Feng, W. Zhang, et al, ”Beating frequency tunable dual wavelength erbium-doped fiber laser with one fiber Bragg grating,” IEEE Photon.Technol. Lett. 16(6): 1453-1455 (2004) L. Sun, X. Feng, Y. Liu, et al. ”Moiré fiber Bragg grating written onprestrained fibers,” Chinese Phys. Lett. 21(4): 669-670, (2004)Conference Presentations L. Sun, S. Jiang, and J. Marciante, ”All-fiber optical Faraday mirror,”CLEO 2010, paper CMGG4
iv L. Sun, S. Jiang, and J. Marciante, ”All-fiber optical magnetic field sensorbased on Faraday rotation,” OFC 2010, paper OWL3 L. Sun, S. Jiang, and J. Marciante, ”Compact all-fiber optical Faradayisolator,” post-deadline, Photonics West 2010, paper 7580-113 L. Sun, S. Jiang, J. Zuegel, and J. Marciante, ”All-fiber isolator based onFaraday rotation,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2009), paper FTuD5 L. Sun, S. Jiang, J. Zuegel, and J. Marciante, ”Measurement of the Verdetconstant in a Terbium-core-doped Fiber,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2008), paper FWR2 L. Sun and J. R. Marciante, ”Filamentation analysis in large-mode-areafiber lasers,” in Frontiers in Optics, OSA Technical Digest (CD) (OpticalSociety of America, 2006), paper FThN5Patents Y. Liu, X. Dong, L. Sun, et al, ”Single and Dual Wavelengths Switchable,Wavelength and Wavelength Spacing Tunable Erbium-doped Optical FiberLaser,” Chinese Patent, NO: 200310107066.2, 2004 S. Yuan, W. Zhang, G. Kai, X. Dong, L. Sun, et al, ”Meshed Optical FiberMicrobend Sensor,” Chinese Patent, NO: 200320112295.9, 2004
vAcknowledgmentsThis is a great opportunity to express my respect to Prof. John R. Marciante.I am deeply grateful for his guidance, support, and understanding for my doctoralstudies. I feel fortunate to be under the mentoring of a great advisor for theseyears. Among all the merits of John, his creative thinking, experimental researchexperience, patience in technical writing, project and lab management skills, andhumor impressed me most. I can not count how many times creative sparks weregenerated in our discussions. When I encountered experimental problems, he always found the reasons and helped me avoid detours. John is strict with us onscientific research, but not pushy. He guides us with direction, but does not limitus. He treats us not only as students, but also as friends. His advice in life andcareer development benefit us.I would like to thank Prof. Govind P. Agrawal. I learned fundamental knowledge in fiber optics in his courses and benefited a lot from his wonderful text booksin fiber optics. I am grateful to the members of my thesis committee, Prof. GovindP. Agrawal, Prof. Robert W. Boyd and Prof. Roman Sobolewski, for their valuablesuggestions and questions. I sincerely thank all the faculty and staff members ofthe Institute of Optics. It is your professors that gave me comprehensive trainingin scientific research. Thanks to Joan Christian, Lissa Cotter, Gina Kern, BestyBenedict, Gayle Thompson and Noelene Votens for giving me great support duringmy studies.I am grateful to Dr. Jonathan Zuegel, Prof. David Meyerhofer, and otherscientists at the Laboratory for Laser Energetics (LLE) for their suggestions ontechnical writing and conference presentations. I would like to thank the Illustration Department of LLE for their preparation of my technical writing; KathieFreson, Jennifer Taylor, Lisa Stanzel, Jennifer Hamson, Karen Kiselycznyk andHeidi Barcomb made beautiful figures and fluent text for me. Thanks to SaraBodensteiner for her help in arranging my conference travel.I would like to thank my colleagues in our research group, Zhuo Jiang, WeihuaGuan, Jordan Leidner, Richard Smith, and Haomin Yao, for their help in the laband discussions. The friendship from my classmates and friends in the Instituteof Optics is important to me. Lianghong Yin, Weihua Guan and Li Ding gave me
vigreat help for the first year when I came Rochester.I would like to acknowledge the support of the Frank J. Horton fellowshipfrom the LLE, University of Rochester. This thesis work was supported by theU.S. Department of Energy (DOE) Office of Inertial Confinement Fusion underCooperative Agreement DE-FC52-08NA28302, the University of Rochester, andthe New York State Energy Research and Development Authority. The supportof DOE does not constitute an endorsement by DOE of the views expressed inthis thesis. This work is also supported in part by Wright-Patterson Air ForceResearch Laboratory (AFRL) under contract FA8650-09-C-5433. I would like toacknowledge the technical support of Dr. R. L. Nelson and W. D. Mitchell fromAFRL.I am deeply grateful to my parents for encouraging me to pursue my education,for teaching me the value of experiences, and for their love.
viiAbstractSurface damage is one of the most problematic power limits in high-power fiberlaser systems. All-fiber Faraday components are demonstrated as a solution tothis problem, since they can be completely fusion-spliced into existing systems,eliminating all glass-air interfaces. Beam filamentation due to self-focusing placesanother limit on the peak power attainable from fiber laser systems. The limitsimposed by this phenomenon are analyzed for the first time.The concept of an effective Verdet constant is proposed and experimentallyvalidated. The effective Verdet constant of light propagation in a fiber includescontributions from the materials in both the core and the cladding. It is measuredin a 25-wt% terbium-doped-core phosphate fiber to be 6.2 rad/(Tm) at 1053nm, which is six times larger than silica fiber. The result agrees well with Faradayrotation theory in optical fiber.A compact all-fiber Faraday isolator and a Faraday mirror are demonstrated.At the core of each of these components is an all-fiber Faraday rotator made of a 4cm-long, 65-wt%-terbium-doped silicate fiber. The effective Verdet constant of theterbium-doped fiber is measured to be -32 rad/(Tm), which is 27 larger than thatof silica fiber. This effective Verdet constant is the largest value measured to datein any fiber and is 83% of the Verdet constant of commercially available crystalsused in bulk-optics-based isolators. Combining the all-fiber Faraday rotator withfiber polarizers results in a fully fusion-spliced all-fiber isolator whose isolation ismeasured to be 19 dB. Combining the all-fiber Faraday rotator with a fiber Bragggrating results in an all-fiber Faraday mirror that rotates the polarization state ofthe reflected light by 88 4 .An all-fiber optical magnetic field sensor is also demonstrated. It consists of afiber Faraday rotator and a fiber polarizer. The fiber Faraday rotator uses a 2-cmlong section of 56-wt%-terbium-doped silicate fiber with a Verdet constant of -24.5rad/(Tm) at 1053 nm. The fiber polarizer is Corning SP1060 single-polarizationfiber. The sensor has a sensitivity of 0.49 rad/T and can measure magnetic fieldsfrom 0.02 to 3.2 T.An all-fiber wavelength-tunable laser based on Faraday rotation is proposed.It consists of an all-fiber wavelength-tunable filter in a conventional fiber laser
viiicavity. The filter includes a fiber polarizer and a fiber Faraday mirror in which achirped fiber Bragg grating is directly written onto the 65-wt% terbium fiber. Theytterbium-doped fiber in the laser is gain flattened using a 1030/1090 nm WDMfilter, resulting a net gain ripple that is measured to be less than 0.2 dB from 1047to 1060 nm. The wavelength tuning range of the resulting fiber laser is thereforeexpected to be in this 1047 to 1060 nm range.Filamentation is one of the nonlinear peak-power-threshold limits in high-powerfiber lasers. Starting from the paraxial wave equation, an analytic expression forthe filamentation threshold in fiber lasers is derived using a perturbation method.The occurrence of filamentation is determined by the larger of two thresholds, oneof perturbative gain and one of spatial confinement. The threshold value is arounda few megawatts, depending on the parameters of the fiber.
ixTable of ContentsForeword1Chapter 1Introduction21.1Brief Review of High-Power Fiber Lasers . . . . . . . . . . . . . . .21.2Power-Threshold Limits in High-Power Optical Fiber Lasers . . . .71.2.1Nonlinear Effects . . . . . . . . . . . . . . . . . . . . . . . .71.2.1.1Stimulated Brillouin Scattering . . . . . . . . . . .71.2.1.2Stimulated Raman Scattering . . . . . . . . . . . .91.2.1.3Self-Focusing . . . . . . . . . . . . . . . . . . . . .10Thermal Effects . . . . . . . . . . . . . . . . . . . . . . . . .101.2.2.1Thermal Fracture . . . . . . . . . . . . . . . . . . .101.2.2.2Melting . . . . . . . . . . . . . . . . . . . . . . . .111.2.2.3Thermal Lensing . . . . . . . . . . . . . . . . . . .11Optical Damage . . . . . . . . . . . . . . . . . . . . . . . . .121.3Thesis Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . .121.4Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .141.2.21.2.3Chapter 2Faraday Effect, Magneto-optical Materials, and Magnet Design152.1Faraday Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .152.2Magneto-Optical Materials . . . . . . . . . . . . . . . . . . . . . . .182.2.1Diamagnetic Materials . . . . . . . . . . . . . . . . . . . . .192.2.2Paramagnetic Materials . . . . . . . . . . . . . . . . . . . .20Magnet Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . .212.3
xChapter 3Effective Verdet Constant Model for Optical Fiber293.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .293.2Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .303.3Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .313.4Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34Chapter 4Cleaving and Splicing of Terbium Fiber364.1Cleaving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .364.2Splicing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .404.3Coupling Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . .44Chapter 5All-Fiber Optical Faraday Components485.1All-Fiber Optical Faraday Isolator and Faraday Mirror . . . . . . .485.1.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . .485.1.2Terbium Doped Optical Fiber . . . . . . . . . . . . . . . . .515.1.3All-Fiber Polarizers . . . . . . . . . . . . . . . . . . . . . . .555.1.4All-Fiber Optical Faraday Isolator . . . . . . . . . . . . . . .595.1.5All-Fiber Optical Faraday Mirror . . . . . . . . . . . . . . .615.1.6Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . .66All-fiber Optical Magnetic Field Sensor . . . . . . . . . . . . . . . .675.2.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . .675.2.2Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . .685.2.3Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . .725.2Chapter 6All-Fiber Wavelength-Tunable Continuous-Wave Laser746.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .746.2Working Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . .756.3Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .80Chapter 7Filamentation Analysis in Large-Mode-Area Fiber Lasers82
xi7.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .827.2Theoretical Model and Steady-State Solution . . . . . . . . . . . . .847.3Linear Stability Analysis and Filament Gain . . . . . . . . . . . . .877.4Spatio-Temporal Analysis of Filament Gain in Optical Fiber Laser .897.5Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . .96Chapter 8ConclusionBibliography99101
xiiList of Tables4.1Optimized LDC-200 parameters for terbium fiber cleaving. . . . . .384.2Optimized Fitel S183PM parameters for terbium fiber splicing. . . .437.1Parameters for ytterbium-doped fiber laser calculations. . . . . . . .90
xiiiList of Figures1.1Typical dimensions of different laser geometries[4]. . . . . . . . . . .41.2Double-clad fiber with end pumping and side pumping[2]. . . . . . .51.3Examples of double-clad fiber structures[4]. . . . . . . . . . . . . . .62.1Faraday rotation in a magneto-optical crystal. . . . . . . . . . . . .152.2Excited-state splitting in diamagnetic materials. . . . . . . . . . . .192.3Excited-state and ground-state splitting in paramagnetic materials.192.4Comparison of Verdet constant in various rare-earth ions[67]. . . . .222.5Annular plane used to calculate magnetic field. . . . . . . . . . . . .232.6Dimensional configuration of a magnet tube. . . . . . . . . . . . . .242.7Dimensional configuration of a magnet cuboid. . . . . . . . . . . . .252.8Theoretical (solid) and measured (circle) magnetic density flux distribution Bz along the center axis z of the N35 magnet cuboid, thedashed lines represent the physical ends of the magnet. . . . . . . .2.926Theoretical (solid) and measured (star) magnetic density flux distribution Bz along the center axis z of the N48 magnet tube, thedashed lines represent the physical ends of the magnet. . . . . . . .272.10 Contour plot of magnetic field integration to reach 45 polarizationrotation as functions of magnet length l and outer radius a2 . . . . .3.128Normalized difference between factors Γ and α for single-mode fiberas a function of normalized frequency υ. . . . . . . . . . . . . . . .323.2Experimental configuration of the Faraday rotation measurement. .323.3Measured (star) rotation angle and corresponding curve fit (solid)at 1053 nm along the center axis z. . . . . . . . . . . . . . . . . . .334.1Fitel S323A Precision Cleaver . . . . . . . . . . . . . . . . . . . . .374.2Vytran LDC-200 Cleaver . . . . . . . . . . . . . . . . . . . . . . . .37
xiv4.3Endface image of cleaved 65 wt% Tb fiber . . . . . . . . . . . . . .394.4Endface interferogram of cleaved 65 wt% Tb fiber . . . . . . . . . .404.5Endface image of mechanically cleaved standard silica fiber . . . . .414.6Schematic of fusion splice and mechanical splice . . . . . . . . . . .414.7Fitel S183PM fusion splicer . . . . . . . . . . . . . . . . . . . . . .424.8Pictorially explanation of the Arc Mid Offset . . . . . . . . . . . . .434.9Fusion splice images of different fibers: (a) silica-to-silica, (b) Tbto-silica (good), (c) Tb-to-silica (bad). . . . . . . . . . . . . . . . .454.10 Fresnel transmittance as a function of n2 /n1 . The circle representsthe case of Tb and silica fibers. . . . . . . . . . . . . . . . . . . . .464.11 Coupling efficiency as a function of ω2 /ω1 . . . . . . . . . . . . . . .475.1Operation of a Faraday isolator illustrated in (a) the forward direction and (b) the backward direction. . . . . . . . . . . . . . . . . .5.2Operation of a Faraday mirror illustrated in (a) the forward direction and (b) the backward direction. . . . . . . . . . . . . . . . . .5.34950Measured rotation angle (circle) and corresponding curve fit (solid)of 56 wt% Tb-doped fiber at a wavelength of 1053 nm as a functionof the magnet location along the fiber axis z.5.4. . . . . . . . . . . .52Theoretical rotation angle of 56 wt% Tb-doped fiber at a wavelength of 1053 nm as a function of the N35 magnet location alongthe fiber axis z. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.554Measured rotation angle (circle) and corresponding curve fit (solid)of 65 wt% Tb-doped fiber at a wavelength of 1053 nm as a functionof the magnet location along the fiber axis z. . . . . . . . . . . . . .5.655Measured (dot) and curve fit (line) Verdet constants of the 54 wt%Tb fiber, 56 wt% Tb fiber, 65 wt% Tb fiber and TGG as a functionof T b3 concentration. . . . . . . . . . . . . . . . . . . . . . . . . .565.7Cross-section structure of the SP1060 fiber. . . . . . . . . . . . . . .575.8Cross-section image of the SP1060 fiber. . . . . . . . . . . . . . . .575.9Measured transmission spectra for two orthogonal polarization directions in a 0.3-m-long SP1060 fiber coiled with a 15 cm diameter.585.10 Longitudinal structure of the CSG (Courtesy of Chiral Photonics). .58
xv5.11 Measured insertion loss and extinction ratio for CSG (Courtesy ofChiral Photonics). . . . . . . . . . . . . . . . . . . . . . . . . . . . .595.12 Experimental configuration of the first all-fiber Faraday isolator. . .605.13 Experimental configuration of the second all-fiber Faraday isolator.615.14 The commercial all-fiber Faraday isolator. Photo courtesy of AdValue Photonics. . . . . . . . . . . . . . . . . . . . . . . . . . . . .625.15 Experimental configuration of the first all-fiber Faraday mirror. . .635.16 Polarization state measurement of the input and output light of thefirst Faraday mirror. Triangles and circles are measurement pointsof the input and output light, respectively. Dashed and solid linesare curve-fits of the input and output light, respectively. . . . . . .645.17 Experimental configuration of the second all-fiber Faraday mirror. .655.18 Polarization state measurement of the input and output light of thesecond Faraday mirror. Squares and circles are measurement pointsof the input and output light, respectively. Dashed and solid linesare curve-fits of the input and output light, respectively. . . . . . .665.19 Integration of all-fiber Faraday components. . . . . . . . . . . . . .675.20 Sensing principle of the all-fiber Faraday magnet sensor. . . . . . .695.21 Experimental configuration of the all-fiber magnet sensor. . . . . . .695.22 Theoretical (solid) and measured (circle) magnetic density flux distribution Bz along the center axis z. Dashed lines represent themagnet ends, and the dotted line represents Bav , the magnetic density flux averaged over a 2-cm length along the axis z. . . . . . . . .705.23 Measured (circle) and calculated (solid) relative transmission of theall-fiber magnet sensor. . . . . . . . . . . . . . . . . . . . . . . . . .715.24 Measured (circles) and theoretical (solid) Bav as a function of thez axis. The dashed lines represent the end of the magnet. . . . . . .716.1Configuration of a general wavelength-tunable fiber laser. . . . . . .756.2Configuration of the all-fiber wavelength-tunable filter. . . . . . . .766.3Rotation of polarization states of different wavelengths in the allfiber filter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.477Experimental configuration to measure the Yb-doped fiber gainspectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .78
xvi6.5Measured ASE spectra of the Yb-doped fiber at different pumpcurrents: 800 mA (solid), 300 mA (dashed), 150 mA (dashed-dot)and 100 mA (dot). . . . . . . . . . . . . . . . . . . . . . . . . . . .6.6Experimental configuration used to flatten the Yb-doped fiber gainspectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.779Experimental configuration of the reflective all-fiber wavelengthtunable filter using Tb fiber. . . . . . . . . . . . . . . . . . . . . . .6.979Gain-flattened ASE spectrum of the Yb-doped fiber at 200 mApump current. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.87880Experimental configuration of the all-fiber wavelength-tunable laser. 806.10 Theoretical calculation of the wavelength tuning as a function ofthe magnet location. . . . . . . . . . . . . . . . . . . . . . . . . . .817.1An intense laser beam is focused due to the nonlinear refractive index. 837.2Filamentation is induced by perturbations in a self-focused beamcondition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7.3Infrared image of the top of a broad-area gain region in a semiconductor laser, illustrating the effect of filamentation[156] . . . . . . .7.491Normalized filament gain versus normalized filament spacing andfrequency for dcore 100 µm, Ps 10 M W . . . . . . . . . . . . . .7.790Normalized filament gain versus normalized filament spacing andfrequency for dcore 100 µm, Ps 10 KW . . . . . . . . . . . . . . .7.684The squared second-order bessel solution J22 as a function of fiberradius. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7.58491(a) Normalized filament spacing and (b) normalized gain as a function of the signal peak power for various core diameters: 20 µm (dotted), 50 µm(dashed-dotted), 100 µm(dashed) and 200 µm(solid)(f 10 GHz). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7.892Gain threshold power [NA 0.2 (dashed), NA 0.1 (dashed-dotted),and NA 0.05 (solid with ” ” symbol)] and spatial threshold power[NA 0.2 (solid), NA 0.1 (dotted), and NA 0.05 (dotted with ” ”symbol)] as functions of core diameter for three numerical apertures(f 10 GHz). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .93
xvii7.9(a) non-normalized (b) normalized filament gain and (c) normalizedfilament spacing as a function of the signal peak power for threedifferent cavity length: 0.5 m(solid), 2 m(dotted) and 4m(dasheddotted)(dcore 100 µm, f 10 GHz). . . . . . . . . . . . . . . . .94
1ForewordThe following individuals are collaborators on the work presented in this thesis:Prof. John Marciante from the Institute of Optics, Univ. of Rochester, Dr. ShibinJiang from AdValue Photonics, and Dr. Jonathan Zuegel from Laboratory forLaser Energetics, Univ. of Rochester.In chapter 1, I did the background work, the calculations, and the technicalwriting. Prof. Marciante provided guidance on technical issues and writing.In chapter 2, I did the background work, the calculations, the measurements,and the technical writing. Prof. Marciante provided guidance on technical issuesand writing.In chapter 3, I did the calculations, the measurements, and the technical writing. Dr. Jiang provided the terbium-doped fiber. Prof. Marciante providedguidance on technical issues and writing.In chapter 4, I did the background work, developed the splicing and cleavingprocesses, and did the technical writing. Dr. Jiang provided the terbium-dopedfiber. Prof. Marciante provided guidance on technical issues and writing.In chapter 5, I fabricated the devices, developed the measurement technique,performed the measurements, analyzed the data, and did the technical writing.Dr. Jiang provided the terbium-doped fibers. Prof. Marciante provided guidanceon technical issues and writing. Prof. Marciante and Dr. Zuegel proposed theconcept of the all-fiber isolator.In chapter 6, I developed the concept, performed the calculations and measurements, and did the technical writing. Prof. Marciante provided guidance ontechnical issues and writing.In chapter 7, I did the derivation, the calculations, and the technical writing.Prof. Marciante provided guidance on technical issues and writing.In chapter 8, I wrote the conclusions with guidance from Prof. Marciante.
2Chapter 1Introduction1.1Brief Review of High-Power Fiber LasersLasers have become more and more important since their first demonstration byMaiman in 1960[1]. While originally limited to science and engineering fields, people today can find lasers in every corner of human life, for example, in consumerelectronics, medical and cosmetic surgery, communications, avionics, and printing. As a subfield of lasers, high-power fiber lasers are attracting more and moreattention. Due to the advantages of low weight, small size, robustness, high efficiency, and heat dissipation, high-power fiber lasers will replace chemical lasers,CO2 lasers, and solid-state lasers in most high-power laser applications. Industrialwelding and soldering, and commercial light detection and ranging (LIDAR) arefields in which high-power fiber lasers are mostly being applied[2], [3], [4].The first fiber laser was demonstrated using neodymium-doped fiber, with sidepumping and multi-spatial-mode output, by Snitzer in 1961[5]. In 1973, Stone reported a longitudinally pumped neodymium-doped fiber laser[6]. The longitudinalpump technique had higher efficiency than the side-pump technique, and the output beam was a single-spatial-mode. In the next several decades, researchers dopeddifferent rare-earth ions into optical fiber. The first erbium-doped fiber amplifier (EDFA) was demonstrated by Mears in 1987[7]. The EDFA, together withwavelength-division-multiplexing (WDM), reduced the cost of long-haul communication systems and promoted the boom of telecommunications at the end ofthe 1990’s. Due to its relatively low efficiency, erbium-doped fiber lasers are not
3suitable for high-power applications.Among the rare-earth ions doped in fiber lasers, neodymium (Nd) was thefirst considered as a dopant for high-power fiber lasers, because Nd-doped lasershave low lasing thresholds due to the four-level energy level structure of N d3 .Currently, ytterbium (Yb) is primarily used in high-power fiber lasers. AlthoughY b3 has a quasi-three level energy structure, Y b3 has a lower quantum defectthan N d3 , which means a higher lasing efficiency. There is no ion-quenchingeffect in Yb-doped fiber lasers, which would reduce the lasing efficiency and induceself-pulsing phenomena.Although the first Yb-doped fiber laser was demonstrated by Etzel in 1962[8], itwas not until the 1990s that high-power Yb-doped fiber lasers began to develop ina dramatic manner. The output power of continuous-wave (CW) high-power Ybdoped fiber lasers have already evolved from the mW level[9] to the multi-kilowattlevel[10]. This rapid development is due to the optical communication and semiconductor industry booms at the end of 1990s. Highly transmissive single-modefiber and advanced doping technologies were enabled by the optical communication industry. The semiconductor industry made high-power laser diodes possible,which are necessary for fiber laser pumping.Besides optical fiber, another laser geometry, the thin disk, was proposed byGiesen in 1994[11]. Both thin disk and optical fiber have been regarded as potential high-power laser geometries to replace rods in solid-state lasers. The mostprominent difference between these two geometries and the rod shape is that theyhave a relatively small volume of laser-active material. Fig. 1.1. shows the typicaldimensions of the these three laser geometries[4]. It is clear that the active volumes of the disk and the fiber are approximately the same and are three orders ofmagnitude smaller than that of a rod.The fiber geometry finally stands out from other two competitors because thesurface-to-volume-ratio in optical fiber is much higher than that of the other twogeometries. This feature is especially important in high-power applications, sincethe larger this parameter is, the faster the heat generated in the active volumeby pump absorption can be dissipated. Heat is one of the major power-limitingfactors in high-power fiber lasers and will be discussed in the next section.Another advantage of the fiber geometry is that it has high pump efficiency and
4FiberDiskRodDiameter4 mm8 mm12 micronLengh0.03 cm10 cm2000 cmVolume0.004 cmSurface/Volume66 cmGeometry3-135 cm-15 cm30.004 cm-12500 cmFigure 1.1: Typical dimensions of different laser geometries[4].a diffraction-limited output beam. Most high-power fiber lasers use a double-cladstructure. Unlike standard communication fiber, double-clad fiber has a three layerstructure consisting of a core, an inner cladding, and an outer cladding. The laserbeam propagates in the core and the pump light is confined in the inner cladding,as shown in Fig. 1.2 [2]. The pump light can be coupled into the inner claddingfrom the end or side of double-clad fiber. The double-clad structure is especiallysuitable for laser diode (LD) pumps which have poor beam quality and can not becoupled into the fiber core with high efficiency.The pump light injected into the inner cladding passes the fiber core and interacts with doping ions repeatedly as it travels along the fiber. However, someof the pump light (in terms of optical rays) will not interact with the fiber core.Since these helical rays propagat
nm, which is six times larger than silica fiber. The result agrees well with Faraday rotation theory in optical fiber. A compact all-fiber Faraday isolator and a Faraday mirror are demonstrated. At the core of each of these components is an all-fiber Faraday rotator made of a 4-cm-long, 65-wt%-terbium-doped silicate fiber.
A Faraday cage can help reduce the effect of electromagnetic radiation. Due to the nature of electromagnetic radiation, two different effects occur simultaneously at the conductive enclosure of the Faraday cage. Figure 3 and Figure 4 show the general principle of a Faraday cage when an electric and magnetic field interacts with a Faraday cage.
Faraday cage, shielding, screening, homogenization, harmonic function AMS subject classifications. 31A35, 78A30 1. Introduction. Everybody has heard of the Faraday cage effect, whereby a wire mesh or metal screen serves to block electric fields and electromagnetic waves. Faraday reported his experiments with a twelve-foot mesh cube in 1836 .
Faraday cage, shielding, screening, homogenization, harmonic function AMS subject classifications. 31A35, 78A30 1. Introduction. Everybody has heard of the Faraday cage effect, whereby a wire mesh or metal screen serves to block electric fields and electromagnetic waves. Faraday reported his experiments with a twelve-foot mesh cube in 1836 .
Faraday Cage O. A. Barro O. Lafond H. Himdi Abstract This letter presents a new recon gurable plasma antenna associated with a Faraday cage. The Faraday cage is realized using a uorescent lamp. A patch antenna with a broadside radiation pattern or a monopole antenna with an end- re radiation pat-tern, operating at 2.45 GHz, is placed inside .
which is called Faraday rotator. The basic setup is shown in Fig. 1. Fig. 1. The principle of integral fiber-optic current sensor. The sensor principle is based on the Ampere’s law l v Bl dIμ (9) where μ is the permeability of Faraday rotator material. For diamagnetic and paramagnetic materials holds μ μ0
ative (anomalous) dispersion for light at 1550 nm. The cavity in Fig. 2 uses the Er3 -doped gain ber, DCF3 and DCF38 for positive (normal) dispersion. Propaga-tion loss at splices can be minimized by matching ber core radii or mode size. For example, in Fig. 2 we spliced the following ber sequence: gain ber, DCF38, DCF3, and SMF-28.
DWDM channels are about -15.6dBm and CWDM channels - 11.5dBm. The data rate 2.5Gbps is considered to get the above mentioned results. (a) Fig.2 (a): BER vs Distance for DWDM (b) BER vs Distance for CWDM system at very clear condition (a) (b) Fig.3 (a): BER vs Received power for DWDM (b) BER vs Received power
Advanced Engineering Mathematics Dr. Elisabeth Brown c 2019 1. Mathematics 2of37 Fundamentals of Engineering (FE) Other Disciplines Computer-Based Test (CBT) Exam Specifications. Mathematics 3of37 1. What is the value of x in the equation given by log 3 2x 4 log 3 x2 1? (a) 10 (b) 1(c)3(d)5 E. Brown . Mathematics 4of37 2. Consider the sets X and Y given by X {5, 7,9} and Y { ,} and the .
